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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $A$ and $B$ are square matrices such that $B=-A^{-1} B A,$ then $(A+B)^2=$
  • A
    $O$
  • ✓
    $A^2+B^2$
  • C
    $A^2+2 A B+B^2$
  • D
    $A + B$
✓

Answer

Correct option: B.
$A^2+B^2$
$B=-A^{-1} B A$
$\Rightarrow A B=-A A^{-1} B A$
$\Rightarrow A b=-I B A$
$\Rightarrow A B=-B A$
$\Rightarrow A B+B A=0 \ldots . . .(i)$
Consider,
$(A+B)^2=A^2+A B+B A+B^2$
$(\because A B \neq B A)$
$(A+B)^2=A^2+O+B^2$
$(A+B)^2=A^2+B^2$

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